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of the matching of selected texture-color features. Image texture features are generated via a gray level
co-occurrence matrix, and color features are generated via an image histogram. Since they are computed
over gray levels, color images of the database are first converted to 256 gray levels. For each image of
the database, a set of texture-color features is extracted. They are derived from a modified form of the
gray level co-occurrence matrix over several angles and distances from the image histogram. Five tex-
ture features and one color feature are extracted from the co-occurrence matrix and image histogram.
These features are represented and normalized in attribute vector, then the rough set dependency rules
are generated directly from the real value attribute vector. Then the rough set reduction technique is
applied to find all reducts of the data that contain the minimal subset of attributes associated with a
class label for classification. To measure the similarity between two images, a new distance measure
between two feature vectors based on rough sets is calculated and evaluated.
Problem Definition:
Assume that we have an image database that contains a collection of images
IDB
=
{
I
1,
I
2, ...
I
n
}. Let Q be a query image and be a real inter-image distance between y two images
I
i
and
I
j
. The user can specify a query to retrieve a number of relevant images. Let
m
be the number of im-
ages that are closed to the query
Q
that the user wants to retrieve such that
m < n
. This image retrieval
problem can be defined as the efficient retrieval of the best of
m
images based on
IDB
from a database
on
n
images.
r ough set t heor y: t heoretical
Background
Basically, rough set theory (Hassanien & Ali, 2004; Pawlak, 1991; Pawlak, 1982; Pawlak, Grzymala-
Busse, Slowinski, & Ziarko, 1995; Slowinski, 1995) deals with the approximation of sets that are dif-
ficult to describe with the available information. In a medical application, a set of interest could be the
set of patients with a certain disease or outcome. In rough set theory, the data are collected in a table,
called a decision table. Rows of the decision table correspond to objects, and columns correspond to
attributes. In the dataset, we assume we are given a set of examples with a class label to indicate the
class to which each example belongs. We call the class label the decision attributes, the rest of the at-
tributes the condition attributes. Rough set theory defines three regions based on the equivalent classes
induced by the attribute values: lower approximation, upper approximation, and boundary. Lower ap-
proximation contains all the objects that are definitely classified based on the data collected, and upper
approximation contains all the objects that can probably be classified. The boundary is the difference
between the upper approximation and the lower approximation. So, we can define a rough set as any
set defined through its lower and upper approximations.
On the other hand, the notion of indiscernibility is fundamental to rough set theory. Informally, two
objects in a decision table are indiscernible if one cannot distinguish between them on the basis of a
given set of attributes. Hence, indiscernibility is a function of the set of attributes under consideration.
For each set of attributes, we can thus define a binary indiscernibility relation, which is a collection of
pairs of objects that are indiscernible to each other. An indiscernibility relation partitions the set of cases
or objects into a number of equivalence classes. An equivalence class of a particular object is simply
the collection of objects that are indiscernible to the object in question. Some formal definitions of the
rough sets are given as follows:
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